3. The expression for the surface area of a cylinder is shown below. Which of the following statements best describes the cylinder? Select all that apply. \( S A=2 \pi(4)^{2}+2 \pi(4)(11) \) The height of the cylinder is 11 . The radius of the cylinder is 2 . The radius of the cylinder is 11 . The radius of the cylinder is 4 .

To determine the characteristics of the cylinder from the given surface area expression: \[ S A = 2 \pi (4)^2 + 2 \pi (4)(11) \] Let's break it down: 1. **Standard Formula for Surface Area of a Cylinder:** \[ S A = 2 \pi r^2 + 2 \pi r h \] - \( r \) = radius of the cylinder - \( h \) = height of the cylinder 2. **Comparing the Given Expression to the Standard Formula:** - The term \( 2 \pi (4)^2 \) corresponds to \( 2 \pi r^2 \), implying that \( r = 4 \). - The term \( 2 \pi (4)(11) \) corresponds to \( 2 \pi r h \), where \( r = 4 \) and \( h = 11 \). 3. **Conclusion:** - **Height (\( h \)) of the cylinder:** 11 - **Radius (\( r \)) of the cylinder:** 4 **Correct Statements:** - The height of the cylinder is 11. - The radius of the cylinder is 4. **Incorrect Statements:** - The radius of the cylinder is 2. - The radius of the cylinder is 11. **Final Answer:** - The height of the cylinder is 11. - The radius of the cylinder is 4.